Interferometers are commonly used for measuring surface flatness. Fringe patterns of interferograms are interpreted to produce detailed topographical maps of artifact surfaces. The detailed topographical information can be further processed to yield first order characteristics of the measured surfaces, including overall position and orientation.
For example, a single interferogram can be interpreted to produce relative measures of thickness variations, such as taper, in transparent artifacts having opposite side surfaces that are optically smooth and nearly parallel. Deformable artifacts can be pressed against a reference surface for determining taper by comparing a measure of an opposing side surface to the reference surface.
However, separate measures of opposite side surfaces are required to measure taper of many artifacts, especially rigid artifacts that are opaque or rough or have nonparallel measurement surfaces. The opposite side surfaces of such artifacts can be separately measured by alternately mounting the opposite side surfaces in a freestanding state (e.g., on a three-point stand). Taper is calculated by comparing the relative orientations of the opposite side surfaces.
We have encountered two problems with making such freestanding measurements of artifact taper on three-point stands. First, irregularities in artifact surfaces mounted on the three-point stands can introduce errors into the measurements. Second, angular deviations in the positions of the three-point stands from assumed reference positions cause further errors. Although it is possible to eliminate these latter-mentioned errors by accurately calibrating the positions of the three-point stands, such calibrations can be difficult and time consuming and are not practical when it is necessary to frequently adjust the three-point stands to accommodate different size or shape artifacts.